VISCOUS FLOW  

TURBULENT FLOW THROUGH PIPES

Unlike fully developed laminar flow in pipes, turbulent flow occurs more frequently in many practical situations. However, this phenomenon is more complex to analyze. Hence, many empirical relations are developed to understand the characteristics of common flow problems. Before, going into these solutions and empirical relations, first few concepts and characteristics of turbulent flows are discussed.

Transition from Laminar to Turbulent Flow
Consider a situation in which a water reservoir is connected to a pipe. The water is initially at rest and is allowed to flow through pipe and the flow rate is regulated by a valve. By opening the valve slowly, the flow velocity and hence the Reynolds number increases from zero to the maximum steady state value. For initial time period, the Reynolds number is small enough for laminar flow to occur. At some time, when the Reynolds number reaches 2100, intermittent spots and random fluctuations appear indicating the flow transition to turbulent condition. This process continues till the Reynolds number value reaches 4000 beyond which the flow becomes fully turbulent.
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